Inswinger and outswinger controversy
= Introduction = One of the big controversies surrounding the study of late Roman (usually metal-framed ballistas) is how their arms operate. There have traditionally been two camps: those who claim these metal-framed ballistas were outswingers and those who claim they were inswingers. In an outswinger the arms of the ballista point away from the case and slider in ~80 degree angle before pulling back the bowstring. When the bowstring is pulled back, the tips of the arm rotate inwards, towards the side of the case and slider. In an inswinger the arms initially point towards the target and are pulled back through the field-frame, tips of the arms almost touching each other in the process. As mentioned here, most of existing research leans heavily on interpretation of ambiguous ancient texts and diagrams. The inswinger theories, on the other hand, lean heavily on archaeological finds. Wilkins (2000: 100) has criticized the inswinging theory on several points. First, he claims that the arms of a P.H.'s cheiroballistra have to be shortened or they will clash. This is not true, unless one lengthens the metal hooks of the arms like he did (see Wilkins 1995 & 2003). P.H. states that the "cone-shaped parts" have to be 11 dactyls long (e.g. Marsden 1971: 217; Wilkins 1995: 32). The little ladder "boards" to which the field-frames are attached are 26 dactyls and 24 dactyls long, respectively. In addition, (apparently) 2 dactyl long tenons are attached to their ends (Marsden 1971: 215; Wilkins 1995: 28). The tenons were probably made similarly to the flattened and punched sections of the Orsova kamarion (Baatz 1978: 11) and were attached to the loops in field-frames. In any case the outer edges of the cord bundles are roughly 24,5 dactyls away from each other. The arms need to be pushed through the cord bundle and a little beyond. This means that when facing each other (perpendicular to the case and slider) their hooked tips (assumed 1,5 dactyls long) are ~4 dactyls away from each other. This is more than enough clearance. = Operating characteristics of an inswinger = If the arms of a ballista are inswinging, they can travel a much wider arc (up to 170 degrees) than in an outswinging configuration (60-70 degrees). In an inswinger, the curved parts of the field-frame bars can be cushioned to stop the arm. Although it would be technically possible to stop the arms of an outswinger similarly, it would not yield any benefits. Therefore the heel pad mentioned by Heron (e.g. Marsden 1971: 29) is used instead. This means that in an inswinger the arm does not have to be pushed as far through the cord bundle, because there's no need for a heel. Interestingly the curved parts of the Gornea field-frames are especially wide. Although this widening does serve other purposes too, it also helps cushioning the blow of the arm effectively. The extra arm travel means that the torsion bundles in an inswinger can store up to 2,5 times the energy of an outswinger if the cord bundle can take it. Also, the bowstring movement characteristics in inswingers and outswingers are quite different. Let's take an inswinger CAD model built according to P.H.'s dimensions as an example: * When arm rotates from 0 to 25 degrees, the string moves 4,7 dactyls forward * When arm rotates from 25 to 50 degrees, the string moves 5,3 dactyls forward * When arm rotates from 50 to 75 degrees, the string moves 2,0 dactyls forward * When arm rotates from 75 to 100 degrees, the string moves 15,0 dactyls forward Somewhere between 50-75 degrees the acceleration of the bowstring stops momentarily. However, as the arms themselves have accelerated for the whole duration of the shot, the last fourth (75->100 degrees) takes a lot less time than the first fourth (0->25 degrees). This means that the bowstring's acceleration at the very end is ridicuously high. Apparently (=testing needed) this final phase of arm movement is critical for the velocity of the bolt. However, this rapid acceleration of the string (and bolt) comes at the cost of reducing the leverage of the arms. This means the bolts have to be light to benefit. The general characteristics of the arm/bowstring movement are shown here: Note that the above picture is not 100% accurate representation of P.H. cheiroballistra. As the arm movement is split to three parts, the incredible arm acceleration during last phase is not immediately visible. Wilkins (2000: 100) claims that in an inswinger the bolt leaves the slider before the arms have moved through their whole arc. His argument is that when the arms are moving outwards (away from the slider) during last half of their travel (in degrees), the forward movement of the string slows down and bolt thus leaves the slider. Wilkins is clearly confused about interaction of the bowstring and the arm as well as basic physics: * The arms accelerate until the heels (or the bowstring) stops them * The bowstring's (and thus bolt's) acceleration at any given point depends on ** arm acceleration (at that point) ** the amount of leverage given by arm/bowstring geometry (at that point) * Bowstring and the bolt maintain most of their forward momentum regardless of what the arms are doing. They only lose momentum through friction and air resistance, to which they are both subject. Even though bowstring's and bolt's acceleration does stop (see above) for a while, the bolt and bowstring travel together, most of the time accelerating, until the very end. In theory, if the combined air resistance and friction of the bolt was much smaller than that of the bowstring, the bolt could - for a few milliseconds - travel ahead of the bowstring. However, the string would very soon catch up. The last phase of arm movement (see above) would more than make up for this. Wilkins also criticized the inswinger design by claiming that in it the bowstring travels only about half of that allowed by conventional arms (Wilkins 2000: 100). This claim has no basis. Wilkins apparently reached this conclusion by using his s.c. "shortened" (=correct length) arms on the inswinger mock-up and overly long arms on his real, operating outswinger. This obviously allows the outswinger bowstring to be pulled back much further. If same length arms (cone 11d long and hook 1,5d long) are used in both outswinger and inswinger configurations, the inswinger wins by a clear margin: * Inswinger with initial arm angle of 9,48 degrees from parallel to slider, measured outwards from the slider. 134 degree rotation and bowstring 28,14 dactyls long. Visualized in the picture above. Total bowstring travel 27,36 dactyls. * Outswinger with initial arm angle 16,82 degrees from perpendicular to slider, measured outwards from the slider. 70 degree rotation and bowstring 43,53 dactyls long. Visualized in the picture below. Total bowstring travel 24,16 dactyls. Although 134 degrees is a close to the maximum for an inswinger, so is 70 degrees for an outswinger. Marsden (1971: 231) estimated that an outswinging cheiroballistra would allow 59 degrees of arm travel and Wilkins (2003: 49) managed to increase that to 70 degrees only by rotating the tenons at the ends of the little ladder beams by 18 degrees. It is also possible that Wilkins meant to say that "for given amount of arm rotation inswinger's bowstring moves forward little less than half that of an outswinger's bowstrings". This is of course true, but does not change the fact that inswinger's springs are capable of storing almost double the energy. Also, widening the inswinger's frame would allow longer draw with same amount of rotation. = Operating characteristics of an outswinger = An outswinger's bowstring accelerates more linearly. This is visualized in this picture: The above cheiroballistra's bowstring/arm travel in numbers: The tip of the arm moves ~1,67 dactyls for every 10 degrees of rotation.As the bowstring is pulled back, the pull is initially very smooth but gets stiffer and stiffer. This what archers call stack and is caused by decrease of leverage from 4:1 (at 0-10 degrees) to 1:1 (at 60-70 degrees). This also means that leverage of the arms upon the bowstring (and bolt) reduces as the bowstring travels forward during launch. The same happens in a much more dramatic fashion with an inswinger (see above). = Case for inswingers = Ancient texts TODO: Describe Iriarte's (2003) inswinger theories here. The Hatra ballista The Hatra ballista is probably the most conclusive piece of evidence for inswinger proponents. The thorough description of the find along with a reconstruction was published by Baatz (1978). The Hatra ballista contained 8 close ended bronze corner fittings. Half of these were "mirrored" but otherwise the same as the other half. The fact that these corner fittings were close-ended means that they could only have been attached to the end of a beam (e.g. a side stanchion). The drawings in Baatz's article clearly show that each corner of the Hatra ballista frame had one of these fittings. Furthermore, Wilkins (2003: 68) provides a additional few excavation/conservation photos which too make this clear. In a nutshell, there were two vertical side stanchions at each end of the Hatra ballista frame and the bronze corner fittings were attached to their ends. It is very difficult to explain the corner fittings in any other way. This is what effectively forces the Hatra ballista to be an inswinger rather than outswinger. To circumvent this problem (if he was indeed aware of it) Wilkins (2003: 68) moved the inner side stanchion towards the middle of the frame. This allowed him to force the Hatra ballista to fit his outswinger theory at the cost of ignoring the inner corner fittings which had been attached to vertical beams. And if the vertical beams didn't go from bottom to the top, they serve absolutely no purpose. Other archaeological finds Since Marsden (1971) several field-frames, kamarions and other parts have been found from Gornea, Lyon, Sala and Orsova. It is not possible to use any of the archaeological field-frames for an outswinger, unless one does both of the following: # Assumes the curve in the curved field-frame bar has suddenly changed it's purpose. The purpose of this bar is to allow the arm to recoil further (Heron, Bel. W. 91-93). # Makes up some very imaginative solution to explain the location of the Pi-brackets in the field-frames. At this point it's necessary to refute Wilkins' locking rings and the chain of arguments leading to them, because those locking rings were designed by Wilkins to solve the above issues. Below one of the problems Wilkins (1995: 21) was trying to solve with his locking rings; above it a very simple solution to the same problem: Notice the construction of the slider (discussed in detail here) and the level of the bowstring. If the slider is constructed from two pieces the bowstring will rub against the slider instead of traveling on top of it. This of course causes friction which eats away bolt velocity and is generally a bad idea. Wilkins assumed that the bars had tenons and counted them as part of their length (10,5 d). This effectively shortened the field frames by 1,5-2 d, depending on how far above the ring the tenons projected before being riveted. This moved the bowstring down towards the slider. Why tenons, then? Wilkins' own translation (1995: 17) says "to attach", not "to rivet". Marsden (forcibly?) translates the same verb as "to weld" (1971: 215). Wilkins' main argument is that somehow a welded joint would be too weak (Wilkins 1995: 19), when actually the contrary is true: a proper forge welding produces joints that are as strong as the materials welded together, unlike in "powerful 20th century welds" (Wilkins 1995: 36). Also, Wilkins (1995: 19) used the existence of tenons in the bars of the Gornea field-frames as proof of tenons in cheiroballistra field-frame bars. However, the tenons in Gornea field-frames only prove that the Gornea field frames were riveted together. Both welding and riveting would be equally possible for the cheiroballistra, except for the fact that P.H. does not talk about tenons or riveting at all. As a summary, Wilkins' shortening of the bars is very risky. Even if Wilkins is correct, it does not negatively affect the solution presented in the upper picture above. Also, Wilkins chose to make his slider from two parts, the upper one having the height (1,25 d) stated by P.H. This means that his slider was 1 dactyl higher than if it was made from one piece. Why did he not see the most obvious solution to this problem? First, we should not forget that Wilkins (1995; 2000; 2003) had decided beforehand that the cheiroballistra was a winched, outswinging weapon. This left him with little choice but forcibly fit the source material to fit his expectations. The most likely reason why Wilkins could not use a one-piece slider was it's small size: it is very hard or even impossible to attach winch ropes and a strong triggering mechanism to a slider whose surface is only 0,25 d above the case, 2 d wide at the bottom and ~1,3-1,5 d wide at the top. A slider resting on top of the case is much more convenient in this regard. Apparently the 2 d wide slider was not strong enough, so Wilkins arbitrarily widened it from 2 d to 2,5 d (Wilkins 1995: 11). Iriarte (2000: 63, 66) tested how these existing kambestria (field-frames) finds would have worked in the outswinger configuration. The results were mixed, with maximum arm travel between 38 and 68 degrees. In an inswinger configuration with same kambestria the arm travel was between 66 and 125 degrees - roughly double that in the inswinger configuration. Iriarte (2000) initially reconstructed his cheiroballistra as an outswinger, but later (2003) "changed camps" in his "The Inswinger Theory" article. TODO: Discuss previous cheiroballistra outswinger reconstructions and point out issues that arise when ignoring archaeological finds. = Case for outswingers = = References = References can be found from the bibliography page. Category:backup